The fuel filter on your Civic is mounted in the top of the fuel tank; removing the fuel tank is required to gain access to the filter. These filters are designed to last the life of the vehicle and do not normally require replacement. With the symptom you describe it is not likely that the fuel filter is teh cause of the problem; filters do not suddenly clog up when the car runs out of fuel.
Teh most likely cause of the no-start problem is a damaged fuel pump (also located inside the gas tank). Electric fuel pumps depend on liquid fuel for cooling and also for lubrication; running an electric pump out of gas can cause internal damage to the pump.
What you can try is banging on the fuel tank while someone tries to start the car; sometimes a sticking pump can be jarred free and start to oeprate again with a little vibration. Even if it does start doing this, the pump should still be replaced as it will happen again at some time without any warning once damage has occurred.